Modelling of Quantum Networks

TL;DR

This paper introduces an analytic perturbation method for quantum networks, enabling the calculation of the scattering matrix using the Dirichlet-to-Neumann map, advancing understanding of quantum network behavior.

Contribution

It presents a novel analytic perturbation technique for quantum networks and derives the scattering matrix via the Dirichlet-to-Neumann map of an intermediate operator.

Findings

Developed an analytic perturbation technique for the absolutely continuous spectrum.

Calculated the scattering matrix for Schrödinger operators on quantum networks.

Connected the Dirichlet-to-Neumann map with scattering matrix computation.

Abstract

We develop the analytic perturbation technique on the absolutely continuous spectrum and calculate the Scattering matrix for the Schr\"{o}dinger operator on the Quantum Network based on the Dirichlet-to Neumann map of an Intermediate operator.